2z^2+10z=z^2-21

Solution for 2z^2+10z=z^2-21 equation:

Simplifying
2z2 + 10z = z2 + -21

Reorder the terms:
10z + 2z2 = z2 + -21

Reorder the terms:
10z + 2z2 = -21 + z2

Solving
10z + 2z2 = -21 + z2

Solving for variable 'z'.

Reorder the terms:
21 + 10z + 2z2 + -1z2 = -21 + z2 + 21 + -1z2

Combine like terms: 2z2 + -1z2 = 1z2
21 + 10z + 1z2 = -21 + z2 + 21 + -1z2

Reorder the terms:
21 + 10z + 1z2 = -21 + 21 + z2 + -1z2

Combine like terms: -21 + 21 = 0
21 + 10z + 1z2 = 0 + z2 + -1z2
21 + 10z + 1z2 = z2 + -1z2

Combine like terms: z2 + -1z2 = 0
21 + 10z + 1z2 = 0

Factor a trinomial.
(7 + z)(3 + z) = 0

Subproblem 1
Set the factor '(7 + z)' equal to zero and attempt to solve:

Simplifying
7 + z = 0

Solving
7 + z = 0

Move all terms containing z to the left, all other terms to the right.

Add '-7' to each side of the equation.
7 + -7 + z = 0 + -7

Combine like terms: 7 + -7 = 0
0 + z = 0 + -7
z = 0 + -7

Combine like terms: 0 + -7 = -7
z = -7

Simplifying
z = -7
Subproblem 2
Set the factor '(3 + z)' equal to zero and attempt to solve:

Simplifying
3 + z = 0

Solving
3 + z = 0

Move all terms containing z to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + z = 0 + -3

Combine like terms: 3 + -3 = 0
0 + z = 0 + -3
z = 0 + -3

Combine like terms: 0 + -3 = -3
z = -3

Simplifying
z = -3
Solution
z = {-7, -3}